A117959 Perrin numbers which are divisible by their digital root.

2, 3, 5, 7, 10, 12, 39, 90, 486, 1130, 1497, 1983, 3480, 4610, 10717, 24914, 33004, 57918, 76725, 134643, 178364, 549289, 727653, 1691588, 2240877, 2968530, 3932465, 5209407, 12110402, 28153269, 65448410, 86700684, 114853953, 1089264462, 1911525877, 3354494070

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..3698

Example

1130 is in the sequence because (1) it is a Perrin number, (2) the digital root is 5 and (3) 1130 is divisible by 5.

Maple

R:= NULL: count:= 0:
a:= 3: b:= 0: c:= 2:
while count < 100 do
  q:= a+b;
  a:= b; b:= c; c:= q;
  dr:= c mod 9; if dr = 0 then dr:= 9 fi;
  if c mod dr = 0 then R:= R, c; count:= count+1;
  fi
od:
sort(convert({R}, list)); # Robert Israel, Mar 16 2023

Mathematica

Select[Union @ LinearRecurrence[{0, 1, 1}, {2, 3, 2}, 100], Divisible[#, Mod[# - 1, 9] + 1] &] (* Amiram Eldar, Feb 06 2021 *)

Crossrefs

Intersection of A001608 and A064807.

Cf. A010888.

Sequence in context: A002822 A191327 A109598 * A117952 A090420 A162999

Adjacent sequences: A117956 A117957 A117958 * A117960 A117961 A117962

Keyword

base,nonn

Author

Luc Stevens (lms022(AT)yahoo.com), May 03 2006

Extensions

Data corrected by Amiram Eldar, Feb 06 2021

Status

approved